We propose to use the steered quantum coherence (SQC) as a signature of quantum phase transitions (QPTs). By considering various spin chain models, including the transverse-field Ising model, XY model, and XX model with three-spin interaction, we showed that the SQC and its first-order derivative succeed in signaling different critical points of QPTs. In particular, the SQC method is effective for any spin pair chosen from the chain, and the strength of SQC, in contrast to entanglement and quantum discord, is insensitive to the distance (provided it is not very short) of the tested spins, which makes it convenient for practical use as there is no need for careful choice of two spins in the chain.

The control of quantum correlations in a physical system is of practical importance. Nonlocal advantage of quantum coherence (NAQC) is a type of quantum correlation defined on the basis of quantum coherence. We present a comparative investigation of NAQC in the threespin Heisenberg model with periodic boundary conditions (PBCs) and topological boundary conditions (TBCs). The results show that while there is no NAQC in the absence of an external magnetic field, one can create a considerable NAQC by applying a nonuniform transverse magnetic field to the three spins. In particular, the NAQC is significantly improved for the model with TBCs compared to that with PBCs, and the regions of nonvanishing NAQC can also be extended. The model considered with TBC can therefore serve as a potential candidate for creating NAQC.

Quantum correlations in a state can be quantified from different aspects. The nonlocal advantage of quantum coherence (NAQC) captures quantum correlation stronger than entanglement and Bell nonlocality. We investigate the NAQC-type quantum correlation in the Heisenberg XY model and showed that both the anisotropy of the interaction between two spins and the external transverse magnetic field can serve as efficient parameters for tuning the NAQC-type quantum correlation. In particular, for the relative low temperature case there is a finite parameter region in which the strength of the NAQC-type quantum correlation is of about its maximum 1. We also found there are quantum states for which the NAQCtype quantum correlations defined by the l 1 norm of coherence and the relative entropy of coherence have a different ordering.

Quantum coherence is not only a fundamental notion in quantum theory but also an invaluable resource for quantum information processing. We investigate the nonlocal advantage of quantum coherence (NAQC) in the Heisenberg model, aimed at seeking flexible ways for its control. By considering impurities, or more explicitly, the inhomogeneous spin couplings and nonuniform magnetic field, in such a model, we showed that an efficient nonlocal control of the NAQC can be realized, and there exists a wide impurity parameter region for which the NAQC takes the value a little less than its maximum 1. Moreover, the critical temperature after which the NAQC vanishes can also be enhanced evidently by tuning the impurity parameters.